The aim of this paper is to replace most of the (proven and unproven) group theory of [BS] by elementary combinatorial arguments and defines a new hierarchy of complexity classes “just above <italic>NP</italic””, introducing Arthur vs. Merlin games and proving that it consists precisely of those languages which belong to NP.Expand

Answering a question of Vera Sós, we show how Lovász’ lattice reduction can be used to find a point of a given lattice, nearest within a factor ofcd (c = const.) to a given point in Rd. We prove that… Expand

WJe show that every nondeterministic computational task S(Z, y), defined as a polynomial time relation between the instance x, representing the input and output combined, and the witness y can be modified to a task S such that each instance/witness pair becomes checkable in poly!ogariihmic Monte Carlo time.Expand

An algebraic approach to the problem of assigning canonical forms to graphs by computing canonical forms and the associated canonical labelings in polynomial time is announced.Expand

The main objective is to exploit the analogy between Turing machine (TM) and communication complexity (CC) classes to provide a more amicable environment for the study of questions analogous to the most notorious problems in TM complexity.Expand

It is shown that the class of languages having tow-prover interactive proof systems is nondeterministic exponential time and that to prove membership in languages inEXP, the honest provers need the power ofEXP only.Expand

The Nearest Lattice Vector Problem (in any l/sub p/ norm), the Nearest Code-word Problem for binary codes, the problem of learning a halfspace in the presence of errors, and some other problems are proved.Expand